The correct answer is option 3, the Indian Councils Act of 1909.

Option 1, the Indian Councils Act of 1861, cannot be the shortest-lived experiment because it first introduced the idea of representative bodies, marking a fundamental shift in the way British India was governed, and these changes persisted.

Option 2, the Indian Councils Act of 1892, expanded the legislative councils but did not introduce anything significantly different that could be construed as short-lived.

Option 4, the Government of India Act of 1919, introduced the concept of dyarchy, or dual government, in the provinces and laid the groundwork for future constitutional development. It was not short-lived; rather, it was a prelude to significant changes in the forthcoming years.

On the other hand, the Indian Councils Act of 1909, also known as the Morley-Minto Reforms, was arguably the shortest-lived. It introduced separate Muslim electorates, which led to increased sectarianism and was subsequently viewed as a misguided move. It was soon supplanted by the subsequent changes brought by the Government of India Act of 1919.